Well then, since this seems like an active topic being revisited, I’ll add some opinions of mine:
The Human body is always regenerating, though on a smaller scale than we see in most games and fiction, as our cells repair themselves and such. Do to this, not only Humans, but every living creature has been able to survive for thousands of years, as if we could not naturally heal without modern medicine we would be extinct long before the first book.
Since it is true humans can naturally recover, I believe the player should always regenerate at a smaller scale, of course boosted when resting since physical activities can hamper the healing process.
Does this mean it will be too easy, or wounds can be ignored? No. If a person with a deep wound such as a bite, were to be swinging a weapon, they could reopen the wound, causing many side effects such as pain to bleeding. From here, you can go wild thinking on how the player can suffer from reckless actions while wounded but not crippled.
Than we have mutations, which of course no one wants being obsolete, specifically faster healing ones. If balanced correctly, they won’t be any worse since much fiction uses the idea regeneration is simply cells being able to work faster and harder, like Wolverine of X-Men. This can also include drawbacks, like increased energy or nutrient requirements since the cells will be working harder.
Overall, I’m no expert, but regeneration should be a passive things buffed by sleeping and strengthened by mutations, with risks for the heavily wounded trying to exert themselves.
*Edit: I would also like to say, to make the game not so easy or hard, it could follow a wound system that I briefly talked about. Project Zomboid is an example, as it’s more casual than CDDA, but has more impact I feel when it comes to wounds. The player has to manage them closely, but won’t spends a week in bed because of it. Of course CDDA can expand on the idea, with wounds lasting a little longer and the chance of reinfection or tearing, and medical items should help speed the process up/shorten heal times overall. It would also be nice if bandages got dirty over time, creating a need for wound checks every so often.